Although there are plenty of kinds the symmetry, elementary school school typically presents only reflective symmetry (or “mirror symmetry”). Together a result, school products tend to use the word symmetry together if it had only that one meaning. This short article will emphasis on the one meaning, but illustrate others together well.

You are watching: Which letter does not have a line of symmetry

*

This photograph shows a an easy picture through a mirror inserted along the line of symmetry. The an outcome that one sees — half of the original and the mirror image of that fifty percent — precisely matches the original figure. We say that the original number is “symmetric” with respect to the mirror; it has reflective symmetry.

Reflective symmetry and “line the symmetry”

*

Mirror-symmetric objects have actually at the very least one line of symmetry, a line follow me which the figure can be folded right into two precisely corresponding parts, parts that room mirror photos of every other.

This figure has 2 lines the symmetry: the horizontal heat of symmetry cuts the number into a top and also bottom that space mirror images of every other; the vertical heat of symmetry cut the figure into a left and right that space mirror pictures of each other. The star listed below has 5 lines of symmetry, 5 lines on which it deserve to be folded so the both sides match perfectly.

*
*
*
*
*

A common misconception uncovered even in numerous glossaries and also texts: not all present that divide a figure into two congruent components are currently of symmetry. Because that example, the diagonal of a (non-square) rectangle is not a line of symmetry.

*

When a mirror is placed along the diagonal line of a rectangle, the an outcome does no look the same as the original rectangle, therefore the diagonal line is no a heat of symmetry. This brand-new shape — the mix of the triangular fifty percent of the initial rectangle and its image in the winter — is dubbed a kite.

Mirror Play

Well prior to children begin any kind of formal research of symmetry, playing with mirrors — possibly on sample Block designs the they develop — creates experience and intuition that deserve to serve both their geometric thinking and their artistic ideas. The vivid design over has just vertical and also horizontal lines of symmetry, yet placing a winter on the at an additional angle can create a beautiful brand-new design.

*
The very first figure listed below shows the the letter A has actually a vertical line of symmetry, but it’s quite “tame” play. More intrepid experiments provide other amazing results.

*
*
*
*

The very same is true the the letter M.

*
*
*

Letters prefer B and also D have a horizontal heat of symmetry: their top and bottom parts match.

Some letters, because that example, X, H, and O, have both vertical and also horizontal present of symmetry.

And some, choose P, R, and N, have actually no present of symmetry.

Rotational symmetry

Another symmetry that youngsters sometimes usage in your Pattern Block designs is “Rotational Symmetry.” A figure has rotational the contrary if some rotation (other than a complete 360° turn) produces the same figure. For example, these figures, as soon as rotated simply the appropriate amount — 360°/3 because that the “name” photo and 360°/5 because that the star — look precisely as lock did before rotation.

*
*

The letters, N, Z, and S additionally share that property.

Note that some figures, like the star and also the vivid blob in ~ the top of the page, yet not the letter N, Z, or S, have actually both reflective and also rotational symmetry.

The many symmetric shape

A circle has infinitely many lines the symmetry: any type of diameter lies on a line of symmetry v the facility of the circle. Any kind of rotation of any kind of amount about the facility of the circle also leaves the circle unchanged.

See more: The Parable Of The Pharisee And The Tax Collector Lesson, Parable Of The Pharisee And The Tax Collector

Books because that children

For young children, K-2:Make a larger Puddle make a smaller sized Worm, by Marion WalterFor larger children, grade 2 and up:The mirror Puzzle Book, by Marion Walter

What’s in a word?

The “metry” in symmetry and also geometry and also metric refers to measurement.